For the function f(x)=3x+1, evaluate and simplify.

Question

 f(x+h)−f(x)=

 

Answer 1

The function is f(x)=3x+1, so if "x" = "x+h" you need to find what f(x+h) is. You do this by substituting "x+h" in for x in the original function: f(x+h)=3(x+h)+1--->3x+3h+1. Now that we know what f(x+h) and f(x) are, we just need to put them into our equation, f(x+h)-f(x):

f(x)=3x+1

f(x+h)=3x+3h+1

f(x+h)-f(x)=3x+3h+1-(3x+1)

=3x+3h+1-3x-1

=3h

The answer is 3h.